Generation of a New Coupled Ultra-Short Pulse System from a Group Theoretical Viewpoint: the Cartan Ehresman Connection

Based upon the group theoretical jet bundle formalism introduced by Wahlquist and Estabrook for discussing the complete integrability of soliton systems, we investigate the prolongation structure of Wadati–Konno–Ichikawa isospectral evolution equations. As a result, we unearth a new physical coupled system entailing a hidden structural symmetry SL(3,R) arising in the description of ultra−short pulse propagation in optical nonlinear media. As a matter of fact, we depict a graphical representation of one-breather and two-breather ultra-short pulses in motion with a non-zero angular momentum. By extending the previous study to multidimensional symmetry SL(n,R), we unearth a more general class of multicomponent coupled nonlinear ultra-short pulse system with its associated inverse scattering formulation particularly useful in soliton theory.